- Everybody Has an Axis to Grind (foreshortening of horizontal surfaces)

- Everybody Wants to Go Up (foreshortening of vertical surfaces)

- Everybody Wants to Squeeze In (fitting a large object on a foreshortened surface)

- Everybody Is On The Go (street intersections and foreshortening) - Everybody Loves Doing It (conclusion)

HOW CAN IT POSSIBLY FIT?

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Foreshortening seems to be a major perspective challenge for many students, especially when the foreshortening is extreme. The term “foreshorten” actually explains itself: when an object is thrust “fore”-ward or toward us, its depth appears to “shorten.”﻿

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Everybody Has an AngleOne of the conditions that produces foreshortening is angle-of-view, which is discussed below in "Everybody Has an Angle.”The other condition is the location of a surface relative to some reference location like the horizon, which you will learn more about as you read on.

rule #1The more extreme the angle of view, the more extreme the foreshortening.

The classic example is a door. When shut and seen face-on, the full width of the door is apparent. In Figure-1A, for instance, the door is clearly 5 units across. As the door begins to open, its width seems to shrink. In Figure-1B the door looks to be only 4 units wide, or a mere 4/5 its physical width. The more the door is opened the more the width of its face appears to shrink as foreshortening grows ever more profound (Figures-1C through 1E). When fully opened, foreshortening of the door is so pronounced that its width disappears entirely and only its edge remains visible (Figure-1F).

Everybody Has an Axis to GrindThe second factor in foreshortening is the location of the object relative to a vanishing axis.

There are two vanishing axes. One is a horizontal line commonly referred to as either the “horizon line” (H.L. in the diagrams) or as “eye level” (E.L.). The other is a vertical line that I call the “vertical vanishing axis,” and it is labeled V.A. in the diagrams. Where the two axes cross is the “center-of-vision” (C.V.), or the place where the eyes are focused. Figures-2A through 2C illustrate these various elements.

For the moment, only the horizontal axis is dealt with. Later the vertical axis will also be addressed.

rule #2The closer an object is to an axis-of-vision the more it is foreshortened.

When a horizontal surface like a tabletop is far from the horizon line (H.L.) it looks quite full; only a little foreshortening is evident (Figure-3A). At less distance from the H.L., as in Figure-3B, there is more foreshortening of the tabletop. If it is very near to the horizon, the table is extremely foreshortened (Figure-3C). When level with the horizon, the table’s top is squeezed down to nothing due to the severity of the foreshortening (Figure-3D).

What has occurred in Figure-3 is that the viewer (that’s you) has altered his or her position relative to the table. Figure-3A is equivalent to the viewer standing on a stool and looking downward at the table top. Figure-3B is the view when standing on the floor. The viewer is seated in Figure-3C, and kneeling in Figure-3D.

Everybody Wants to Go UpJust as our perception of a horizontal surface like a tabletop is affected by its location relative to the horizon, our experience of a vertical surface such as a wall is influenced by its proximity to the vertical vanishing axis (V.A.). While the horizontal vanishing axis (horizon line) is even with your eyes (Figure-4A), the vertical vanishing axis aligns with the midline of your body as shown in Figure-4B. And, just as a horizontal surface is increasingly foreshortened the more closely it approaches the horizon line (as illustrated by Figures-3A through 3D), a vertical surface becomes progressively foreshortened as it gets nearer to the V.A. The effect is demonstrated by Figures-5A through 5D.

Notice, incidentally, that the wall dividers in Figures-5A through 5D are identical to the table tops in Figures-3A through 3D, but rotated 90-degrees.

This is all in keeping with the principles discussed above and with Rule #2 as stated above and repeated here:

rule #2The closer an object is to an axis-of-vision the more it is foreshortened.

Everybody Wants to Squeeze InThe most perplexing question about foreshortening is: “How does that huge object fit on that sliver of a surface?” Well, the answer can be found in Rule #3.

rule #3An object mounted on a surface is foreshortened to the same degree as the surface.

In other words, if a tabletop is foreshortened a certain amount, a box perched on the tabletop is foreshortened by the same amount. Take a look at Figures-6A through 6D. The table’s top is more compressed in Figure-6C than in Figure-6B, and so too is the box in Figure-6C. The difference is even more stark as you compare Figure-6C to Figure-6A.

The tabletop in Figure-6D has been foreshortened down to nothing; there seems to be no room for anything on that table! Yet, there is that box nestled there quite comfortably. The reason, simply, is that the base of the box has also been compressed to zero.

An overhead view of this scenerio is presented in Figure-7A. It is clear that the box fits well on the table.

What is not so clear is how that enormous box can squeeze onto the tabletop shown in Figure-7B. It fits because the underside of the box is foreshortened to an equal degree as the table (Figure-7C). When Figure-7B and Figure-7C are combined, as in Figure-7D, it is evident that there is no difficulty getting the box to fit.

Everybody Is On the GoOur final example of foreshortening is a street intersection.

From directly above, a pair of crossing streets might look much like Figure-8A in which both streets are the same width. Figure-8B and Figure-8C represent a view of the same intersection as seen from a nearby hill.

Although it may initially seem acceptable to your eyes, no foreshortening has been applied to the cross-street in Figure-8B. If measured, you will find it is about the same breadth as the main thoroughfare, but it appears broader because of the absence of foreshortening.

Foreshortening has been correctly applied in Figure-8C. If measured, the cross-street as affected by foreshortening is slightly more narrow that the main road, yet it appears to be the proper width.

A scene can be tested by visualizing the intersection as the lid of a cube-shaped box. Figure-9A is identical to Figure-8B, except the intersection has acquired a box-like basement. If foreshortening had been properly employed, the box would have looked like a cube of sugar; instead it resembles a stick of butter.

When proper foreshortening is exploited, like in Figure-9B, the box produced is indeed cube-like.

Everybody Loves Doing ItThe trick to foreshortening, if there is a trick, is to trust your eyes. When a surface is compressed due to foreshortening, even if it is compressed practically to nothing, do not try to force that surface to be more expansive than it really is. Amazingly, the things you see atop it actually do fit!